Equilibrium Point Hypothesis Research Articles

Generalizable and precise control based on equilibrium-point hypothesis for musculoskeletal robotic system

PurposeThe purpose of this study is realizing human-like motions and performance through musculoskeletal robots and brain-inspired controllers. Human-inspired robotic systems, owing to their potential advantages in terms of flexibility, robustness and generality, have been widely recognized as a promising direction of next-generation robots.Design/methodology/approachIn this paper, a deep forward neural network (DFNN) controller was proposed inspired by the neural mechanisms of equilibrium-point hypothesis (EPH) and musculoskeletal dynamics.FindingsFirst, the neural mechanism of EPH in human was analyzed, providing the basis for the control scheme of the proposed method. Second, the effectiveness of proposed method was verified by demonstrating that equilibrium states can be reached under the constant activation signals. Finally, the performance was quantified according to the experimental results.Originality/valueBased on the neural mechanism of EPH, a DFNN was crafted to simulate the process of activation signal generation in human motion control. Subsequently, a bio-inspired musculoskeletal robotic system was designed, and the high-precision target-reaching tasks were realized in human manner. The proposed methods provide a direction to realize the human-like motion in musculoskeletal robots.

Identifying Referent Control Variables Underlying Goal-Directed Arm Movements.

The referent control theory (RCT) for action and perception is an advanced formulation of the equilibrium-point hypothesis. The RCT suggests that rather than directly specifying the desired motor outcome, the nervous system controls action and perception indirectly by setting the values of parameters of physical and physiological laws. This is done independently of values of kinematic and kinetic variables including electromyographic patterns describing the motor outcome. One such parameter-the threshold muscle length, λ, at which motoneurons of a given muscle begin to be recruited, has been identified experimentally. In RCT, a similar parameter, the referent arm position, R, has been defined for multiple arm muscles as the threshold arm position at which arm muscles can be quiescent but activated depending on the deflection of the actual arm position, Q, from R. Changes in R result in reciprocal changes in the activity of opposing muscle groups. We advanced the explanatory power of RCT by combining the usual biomechanical descriptions of motor actions with the identification of the timing of R underlying arm movements made with reversals in three directions and to three different extents. We found that in all movements, periods of minimization of the activity of multiple muscles could be identified at ∼61%-86% of the reaching extent in each direction. These electromyographic minimization periods reflect the spatial coordinates at which the R and Q overlap during the production of movements with reversals. The findings support the concept of the production of arm movement by shifting R.

Intra-limb Coordination and Control in Individuals with Stroke: Conceptual and Methodological Considerations

Background: A substantial amount of descriptive, rehabilitation and review research examined the behavioral (kinematic) nature of intra-limb organization in reaching and grasping actions in individuals who suffered a stroke. However, the majority of this work failed to explicitly address the level of movement organization affected, the conceptual relevance to existing theories of motor control, and the impact of different constraints on the emerging actions. Thus, the purpose was to examine whether the selected studies examined the issue in coordination and/or control, in the context of the existing conceptual frameworks. The second purpose was to delineate which individual and task constraints have been examined in previous work, and infer the degree to which these factors affected the nature of the emerging movement patterns. Methods: The search of four databases (PubMed, Embase, Web of Science and CINAHL), including published work between January 2019 and March 2022, yielded twenty studies. Results: Despite the fact that stroke substantially alters the emerging movement patterns majority of the studies examined issues in control, not coordination. In term of spatial and temporal control, the actions of individuals with stroke were slower and involved minimal use of the shoulder and elbow joints, as compared to their healthy counterparts. The analysis of emerging movement patterns, via inverse kinematics, showed that stroke resulted in segmented coordination between shoulder and elbow, while no studies examined the relations between distal anatomical structures (e.g., elbow and wrist). In terms of specific theories or models of motor control, most research was data-driven as only three studies made inferences to existing motor control theories (e.g., Equilibrium Point Hypothesis). In regards to the second purpose, time after stroke was the most impactful individual constraint which differentiated the nature of movement organization exhibited by those with and without stroke. The impact of variables such as gender and age, on performance of individuals with stroke, was not examined. From the methodological standpoint, lack of measures of intra-individual variability represents an important limitation in rehabilitation research reviewed. Conclusion: Collectively, the understanding of how individuals with stroke organize their actions remains equivocal. This is due to a variety of different methodological approaches used (e.g., forward vs. inverse kinematics), limited insight into critical aspects of movement organization (e.g., coordination) and the effects of key individual constraints (e.g., age/gender) on the nature of emerging movements. Also, the fact that data driven research still represents the primary impetus in this clinical field undermines the validity of the emerging inferences.

Neurorobotics and neuroprostheses: Towards a new anatomy.

The idea of this Special Issue arose from the technological advances in bionic, robotic, and neural rehabilitation systems and the common need to comprehend in detail how human anatomical structures can be replicated or controlled. Motor control theories, among others, include the generalized control program theory, the equilibrium point hypothesis, or the optimal control approach in which neural commands to the muscles are a result of the central nervous system solving an optimization problem for a specific cost function. No matter the alternative interpretation selected to replicate biological control of human movements, artificial "anatomies" should consider not only motor capabilities from the central nervous system but integrate bioinspired mechanical features (such as compliance) in artificial limbs. The development of wearable robotics and neuroprosthetic systems for human movement compensation and control is naturally inspired by human anatomy and biology. Cutting-edge technological advances in the field of biomedical and neural engineering are bringing us more and more close to a new artificial anatomy with which humans could augment their motor capabilities or replace them after they are compromised. Either augmentative/assistive or rehabilitation technologies in the near future will require engineering solutions based on novel approaches to create usable neurorobotic and neuroprosthetic systems for the most relevant societal needs.

Assisting Forearm Function in Children With Movement Disorders via A Soft Wearable Robot With Equilibrium-Point Control.

Wearable robots are envisioned to amplify the independence of people with movement impairments by providing daily physical assistance. For portable, comfortable, and safe devices, soft pneumatic-based robots are emerging as a potential solution. However, due to the inherent complexities, including compliance and nonlinear mechanical behavior, feedback control for facilitating human–robot interaction remains a challenge. Herein, we present the design, fabrication, and control architecture of a soft wearable robot that assists in supination and pronation of the forearm. The soft wearable robot integrates an antagonistic pair of pneumatic-based helical actuators to provide active pronation and supination torques. Our main contribution is a bio-inspired equilibrium-point control scheme for integrating proprioceptive feedback and exteroceptive input (e.g., the user’s muscle activation signals) directly with the on/off valve behavior of the soft pneumatic actuators. The proposed human–robot controller is directly inspired by the equilibrium-point hypothesis of motor control, which suggests that voluntary movements arise through shifts in the equilibrium state of the antagonistic muscle pair spanning a joint. We hypothesized that the proposed method would reduce the required effort during dynamic manipulation without affecting the error. In order to evaluate our proposed method, we recruited seven pediatric participants with movement disorders to perform two dynamic interaction tasks with a haptic manipulandum. Each task required the participant to track a sinusoidal trajectory while the haptic manipulandum behaved as a Spring-Dominate system or Inertia-Dominate system. Our results reveal that the soft wearable robot, when active, reduced user effort on average by 14%. This work demonstrates the practical implementation of an equilibrium-point volitional controller for wearable robots and provides a foundational path toward versatile, low-cost, and soft wearable robots.

The legacy of Gerald L. Gottlieb in human movement neuroscience.

In this paper, we review the legacy of Gerald (Gerry) Gottlieb in various fields related to the neural control of human movement. His studies on the myotatic (stretch) reflex and postmyotatic responses to ankle joint perturbations paved the way for current explorations of long-loop reflexes and their role in the control of movement. The dual-strategy hypothesis introduced order into a large body of literature on the triphasic muscle activation patterns seen over a variety of voluntary movements in healthy persons. The dual-strategy hypothesis continues to be important for understanding the performance of subjects with disordered motor control. The principle of linear synergy (covariance of joint torques) was an attempt to solve one of the notorious problems of motor redundancy, which remains an important topic in the field. Gerry's attitude toward the equilibrium-point hypothesis varied between rejection and using it to explore patterns of hypothetical control variables and movement variability. The discovery of reciprocal excitation in healthy neonates fostered other studies of changes in spinal cord physiology as motor skills develop. In addition, studies of people with spasticity and the effects of treatment with intrathecal baclofen were crucial in demonstrating the possibility of unmasking voluntary movements after suppression of the hyperreflexia of spasticity. Gerry Gottlieb contributed a significant body of knowledge that formed a solid foundation from which to study a variety of neurological diseases and their treatments, and a more comprehensive and parsimonious foundation to describe the neural control of human movement.

A Vexing Question in Motor Control: The Degrees of Freedom Problem.

The human “marionette” is extremely complex and multi-articulated: anatomical redundancy (in terms of Degrees of Freedom: DoFs), kinematic redundancy (movements can have different trajectories, velocities, and accelerations and yet achieve the same goal, according to the principle of Motor Equivalence), and neurophysiological redundancy (many more muscles than DoFs and multiple motor units for each muscle). Although it is quite obvious that such abundance is not noxious at all because, in contrast, it is instrumental for motor learning, allowing the nervous system to “explore” the space of feasible actions before settling on an elegant and possibly optimal solution, the crucial question then boils down to figure out how the nervous system “chooses/selects/recruits/modulates” task-dependent subsets of countless assemblies of DoFs as functional motor synergies. Despite this daunting conceptual riddle, human purposive behavior in daily life activities is a proof of concept that solutions can be found easily and quickly by the embodied brain of the human cognitive agent. The point of view suggested in this essay is to frame the question above in the old-fashioned but still seminal observation by Marr and Poggio that cognitive agents should be regarded as Generalized Information Processing Systems (GIPS) and should be investigated according to three nearly independent but complementary levels of analysis: 1) the computational level, 2) the algorithmic level, and 3) the implementation level. In this framework, we attempt to discriminate as well as aggregate the different hypotheses and solutions proposed so far: the optimal control hypothesis, the muscle synergy hypothesis, the equilibrium point hypothesis, or the uncontrolled manifold hypothesis, to mention the most popular ones. The proposed GIPS follows the strategy of factoring out shaping and timing by adopting a force-field based approach (the Passive Motion Paradigm) that is inspired by the Equilibrium Point Hypothesis, extended in such a way to represent covert as well overt actions. In particular, it is shown how this approach can explain spatio-temporal invariances and, at the same time, solve the Degrees of Freedom Problem.

Pinocchio: A language for action representation

The development of a language of action representation is a central issue for cognitive robotics, motor neuroscience, ergonomics, sport, and arts with a double goal: analysis and synthesis of action sequences that preserve the spatiotemporal invariants of biological motion, including the associated goals of learning and training. However, the notation systems proposed so far only achieved inconclusive results. By reviewing the underlying rationale of such systems, it is argued that the common flaw is the choice of the ‘primitives’ to be combined to produce complex gestures: basic movements with a different degree of “granularity”. The problem is that in motor cybernetics movements do not add: whatever the degree of granularity of the chosen primitives their simple summation is unable to produce the spatiotemporal invariants that characterize biological motion. The proposed alternative is based on the Equilibrium Point Hypothesis and, in particular, on a computational formulation named Passive Motion Paradigm, where whole-body gestures are produced by applying a small set of force fields to specific key points of the internal body schema: its animation by carefully selected force fields is analogous to the animation of a marionette using wires or strings. The crucial point is that force fields do add, thus suggesting to use force fields as a consistent set of primitives instead of basic movements. This is the starting point for suggesting a force field-based language of action representation, named Pinocchio in analogy with the famous marionette. The proposed language for action description and generation includes three main modules: 1) Primitive force field generators, 2) a Body-Model to be animated by the primitive generators, and 3) a graphical staff system for expressing any specific notated gesture. We suggest that such language is a crucial building block for the development of a cognitive architecture of cooperative robots.

A biological-like controller using improved spiking neural networks

This paper is devoted to developing a biological-based algorithm to simulate the control of a human arm by means of a Spiking Neural Network (SNN) with a pre-set structure similar to those found in reflex arcs. The replication of the behavior of biological systems is a primary step to understand how the brain and the neural networks that comprise it work. The study of these systems began with the analysis of animals with low neural complexity as well as with small control neural networks such as those present in the reflex acts of the human body. However, the study of the brain, due to its intricate structure, still presents many unknowns and challenges to be solved. Meanwhile, one way to understand how biological systems work is to emulate their behavior through computer simulations. Artificial neural networks (ANNs) offered the opportunity to replicate neural structures to understand and reproduce their behavior and performance. Many types of ANNs are based on the use of activation functions. However, these ANNs are simplified models that do not replicate the behavior of complex biological neural systems accurately. For this reason, spike-based models have been developed to reproduce real biological systems more faithfully. This work proposes simulating the motor behavior of the central nervous system to control the position of an arm. To this end, a spiking neural network has been developed to emulate motion control using a fixed structure that reproduces reflex arcs. A channel-based synapse model and a control scheme based on the equilibrium point hypothesis have been proposed to improve biological similarity of the controller. Furthermore, the developed controller has learning capabilities thanks to the reproduction of the synapse plasticity process that takes place in real biological systems through a supervised Spike-Timing Dependent Plasticity (STDP) learning strategy. The performance of the proposed approach has been demonstrated by simulating the control of the movement of an arm using Hill’s Muscle Model. Results suggest that the proposed control algorithm resembles the response of biological systems adequately in terms of speed and temporal response.

Motor Control: Creating a Natural Science of Biological Movement

Motor control is a young and aspiring field of natural science. Over the past 40 years, it has become an established field of study with several important theoretical developments, including the equilibrium-point hypothesis and its more recent version known as the control with referent spatial coordinates, the principle of abundance, the uncontrolled manifold hypothesis, and the concept of dynamic neural field as the means of task formulation. Important experimental advances have included the exploration of the notion of synergies, the links between descending signals from the brain and referent coordinates of the effectors, and applications of motor control principles to analysis of disordered movements. Further maturation of motor control requires focusing on theory-driven studies. It promises fruitful applications to applied fields such as movement disorders and rehabilitation.

Trajectory adaptation of biomimetic equilibrium point for stable locomotion of a large-size hexapod robot

This paper proposes a control scheme inspired by the biological equilibrium point hypothesis (EPH) to enhance the motion stability of large-size legged robots. To achieve stable walking performances of a large-size hexapod robot on different outdoor terrains, we established a compliant-leg model and developed an approach for adapting the trajectory of the equilibrium point via contact force optimization. The compliant-leg model represents well the physical property between motion state of the robot legs and the contact forces. The adaptation approach modifies the trajectory of the equilibrium point from the force equilibrium of the system, and deformation counteraction. Several real field experiments of a large-size hexapod robot walking on different terrains were carried out to validate the effectiveness and feasibility of the control scheme, which demonstrated that the biologically inspired EPH can be applied to design a simple linear controller for a large-size, heavy-duty hexapod robot to improve the stability and adaptability of the motion in unknown outdoor environments.

Eye and head movements and vestibulo-ocular reflex in the context of indirect, referent control of motor actions.

Conventional explanations of the vestibulo-ocular reflex (VOR) and eye and head movements are revisited by considering two alternative frameworks addressing the question of how the brain controls motor actions. Traditionally, biomechanical and/or computational frameworks reflect the views of several prominent scholars of the past, including Helmholtz and von Holst, who assumed that the brain directly specifies the desired motor outcome and uses efference copy to influence perception. However, empirical studies resulting in the theory of referent control of action and perception (an extension of the equilibrium-point hypothesis) revealed that direct specification of motor outcome is inconsistent with nonlinear properties of motoneurons and with the physical principle that the brain can control motor actions only indirectly, by changing or maintaining the values of neurophysiological parameters that influence, but can remain independent of, biomechanical variables. Some parameters are used to shift the origin (referent) points of spatial frames of reference (FRs) or system of coordinates in which motor actions emerge without being predetermined. Parameters are adjusted until the emergent motor actions meet the task demands. Several physiological parameters and spatial FRs have been identified, supporting the notion of indirect, referent control of movements. Instead of integration of velocity-dependent signals, position-dimensional referent signals underlying head motion can likely be transmitted to motoneurons of extraocular muscles. This would produce compensatory eye movement preventing shifts in gaze during head rotation, even after bilateral destruction of the labyrinths. The referent control framework symbolizes a shift in the paradigm for the understanding of VOR and eye and head movement production.

Bio-Inspired Equilibrium Point Control Scheme for Quadrupedal Locomotion

The goal of this paper is to present a force control scheme for quadrupedal locomotion by adopting observations of biological motor behavior. Specifically, based on the equilibrium point (EP) hypothesis, we set up a bio-inspired EP controller in Cartesian space. The proposed EP controller modifies the EP trajectories appropriately over time from two perspectives, which can ensure stable interactions and system equilibrium. One perspective is directly compensating for the posture angle error based on torso posture compensation. The other is based on the foot force tracking algorithm and admittance model. The main contribution of this paper is to show how the EP controller realizes dynamic balance with no input about inertial parameter identification for the robot or terrain information estimation. Overall, the EP control scheme is simplified for stability problems and is easy to use in practice. Finally, we carried out a series of simulations and experiments to evaluate the effectiveness of the EP control algorithm. The results demonstrate that the proposed controller may improve dynamic stability and realize compliance performance.

Passive motion and active inference: Commentary on “Muscleless motor synergies and actions without movements: From motor neuroscience to cognitive robotics” by Vishwanathan Mohan, Ajaz Bhat and Pietro Morasso

Mohan et al offer an exhaustive and compelling survey of different paradigms for understanding an embodied exchange with the world. They describe a new way of looking at motor control that has emerged over the past years, – a view that resolves many issues with previous (optimal motor control) formulations. Pleasingly, this new way of looking at things picks up on historical themes that date back to the 19th century. For example, notions of synergy formation and the equilibrium point hypothesis, re-emerge with a new simplicity and explanatory power, when one takes a holistic and enactive view of embodied behaviour. Indeed, one might trace the ideas explored in Mohan et al back to foundational notions enshrined in ideomotor theory and Helmholtz's notion of unconscious inference. This new way of looking at things is centred on the notion of a forward or generative model that plays the functional role of a “plastic configurable internal representation of the body (body schema) as a critical link enabling the seamless continuum between motor control and imagery.” Mohan et al.

Indirect, referent control of motor actions underlies directional tuning of neurons.

Many neurons of the primary motor cortex (M1) are maximally sensitive to "preferred" hand movement directions and generate progressively less activity with movements away from these directions. M1 activity also correlates with other biomechanical variables. These findings are predominantly interpreted in a framework in which the brain preprograms and directly specifies the desired motor outcome. This approach is inconsistent with the empirically derived equilibrium-point hypothesis, in which the brain can control motor actions only indirectly, by changing neurophysiological parameters that may influence, but remain independent of, biomechanical variables. The controversy is resolved on the basis of experimental findings and theoretical analysis of how sensory and central influences are integrated in the presence of the fundamental nonlinearity of neurons: electrical thresholds. In the presence of sensory inputs, electrical thresholds are converted into spatial thresholds that predetermine the position of the body segments at which muscles begin to be activated. Such thresholds may be considered as referent points of respective spatial frames of reference (FRs) in which neurons, including motoneurons, are centrally predetermined to work. By shifting the referent points of respective FRs, the brain elicits intentional actions. Pure involuntary reactions to perturbations are accomplished in motionless FRs. Neurons are primarily sensitive to shifts in referent directions, i.e., shifts in spatial FRs, whereas emergent neural activity may or may not correlate with different biomechanical variables depending on the motor task and external conditions. Indirect, referent control of posture and movement symbolizes a departure from conventional views based on direct preprogramming of the motor outcome.

Muscle coactivation: definitions, mechanisms, and functions.

The phenomenon of agonist-antagonist muscle coactivation is discussed with respect to its consequences for movement mechanics (such as increasing joint apparent stiffness, facilitating faster movements, and effects on action stability), implication for movement optimization, and involvement of different neurophysiological structures. Effects of coactivation on movement stability are ambiguous and depend on the effector representing a kinematic chain with a fixed origin or free origin. Furthermore, coactivation is discussed within the framework of the equilibrium-point hypothesis and the idea of hierarchical control with spatial referent coordinates. Relations of muscle coactivation to changes in one of the basic commands, the c-command, are discussed and illustrated. A hypothesis is suggested that agonist-antagonist coactivation reflects a deliberate neural control strategy to preserve effector-level control and avoid making it degenerate and facing the necessity to control at the level of signals to individual muscles. This strategy, in particular, allows stabilizing motor actions by covaried adjustments in spaces of control variables. This hypothesis is able to account for higher levels of coactivation in young healthy persons performing challenging tasks and across various populations with movement impairments.

Test of Human Finger-joint Movement Model Using Functional Electrical Stimulation Based on Equilibrium Point Hypothesis under an Isometric Condition

Test of Human Finger-joint Movement Model Using Functional Electrical Stimulation Based on Equilibrium Point Hypothesis under an Isometric Condition

Stability of Kinesthetic Perception in Efferent-Afferent Spaces: The Concept of Iso-perceptual Manifold

The main goal of this paper is to introduce the concept of iso-perceptual manifold for perception of body configuration and related variables (kinesthetic perception) and to discuss its relation to the equilibrium-point hypothesis and the concepts of reference coordinate and uncontrolled manifold. Hierarchical control of action is postulated with abundant transformations between sets of spatial reference coordinates for salient effectors at different levels. Iso-perceptual manifold is defined in the combined space of afferent and efferent variables as the subspace corresponding to a stable percept. Examples of motion along an iso-perceptual manifold (perceptually equivalent motion) are considered during various natural actions. Some combinations of afferent and efferent signals, in particular those implying a violation of body's integrity, give rise to variable percepts by artificial projection onto iso-perceptual manifolds. This framework is used to interpret unusual features of vibration-induced kinesthetic illusions and to predict new illusions not yet reported in the literature.

Unsteady steady-states: central causes of unintentional force drift.

We applied the theory of synergies to analyze the processes that lead to unintentional decline in isometric fingertip force when visual feedback of the produced force is removed. We tracked the changes in hypothetical control variables involved in single fingertip force production based on the equilibrium-point hypothesis, namely the fingertip referent coordinate (R FT) and its apparent stiffness (C FT). The system's state is defined by a point in the {R FT; C FT} space. We tested the hypothesis that, after visual feedback removal, this point (1) moves along directions leading to drop in the output fingertip force, and (2) has even greater motion along directions that leaves the force unchanged. Subjects produced a prescribed fingertip force using visual feedback and attempted to maintain this force for 15s after the feedback was removed. We used the "inverse piano" apparatus to apply small and smooth positional perturbations to fingers at various times after visual feedback removal. The time courses of R FT and C FT showed that force drop was mostly due to a drift in R FT toward the actual fingertip position. Three analysis techniques, namely hyperbolic regression, surrogate data analysis, and computation of motor-equivalent and non-motor-equivalent motions, suggested strong covariation in R FT and C FT stabilizing the force magnitude. Finally, the changes in the two hypothetical control variables {R FT; C FT} relative to their average trends also displayed covariation. On the whole, the findings suggest that unintentional force drop is associated with (a) a slow drift of the referent coordinate that pulls the system toward a low-energy state and (b) a faster synergic motion of R FT and C FT that tends to stabilize the output fingertip force about the slowly drifting equilibrium point.

Towards a learnt neural body schema for dexterous coordination of action in humanoid and industrial robots

During any goal oriented behavior the dual processes of generation of dexterous actions and anticipation of the consequences of potential actions must seamlessly alternate. This article presents a unified neural framework for generation and forward simulation of goal directed actions and validates the architecture through diverse experiments on humanoid and industrial robots. The basic idea is that actions are consequences of an simulation process that animates the internal model of the body (namely the body schema), in the context of intended goals/constraints. Specific focus is on (a) Learning: how the internal model of the body can be acquired by any robotic embodiment and extended to coordinated tools; (b) Configurability: how diverse forward/inverse models of action can be `composed' at runtime by coupling/decoupling different body (body $$+$$+ tool) chains with task relevant goals and constraints represented as multi-referential force fields; and (c) Computational simplicity: how both the synthesis of motor commands to coordinate highly redundant systems and the ensuing forward simulations are realized through well-posed computations without kinematic inversions. The performance of the neural architecture is demonstrated through a range of motor tasks on a 53-DoFs robot iCub and two industrial robots performing real world assembly with emphasis on dexterity, accuracy, speed, obstacle avoidance, multiple task-specific constraints, task-based configurability. Putting into context other ideas in motor control like the Equilibrium Point Hypothesis, Optimal Control, Active Inference and emerging studies from neuroscience, the relevance of the proposed framework is also discussed.